Time invariant property of weighted circular convolution and its application to continuous wavelet transform

• Autorzy: Yi Hua , Ru Yu-Le , Dai Yin-Yun

Identyfikatory

DOI

10.24425/bpasts.2021.137726

• Języki publikacji: EN

Abstrakty

EN

Time invariant linear operators are the building blocks of signal processing. Weighted circular convolution and signal processing framework in a generalized Fourier domain are introduced by Jorge Martinez. In this paper, we prove that under this new signal processing framework, weighted circular convolution also has a generalized time invariant property. We also give an application of this property to algorithm of continuous wavelet transform (CWT). Specifically, we have previously studied the algorithm of CWT based on generalized Fourier transform with parameter 1. In this paper, we prove that the parameter can take any complex number. Numerical experiments are presented to further demonstrate our analyses.

Słowa kluczowe

EN

continuous wavelet transform; linear convolution; weighted circular convolution; generalized discrete Fourier transform

PL

ciągła transformata falkowa; splot liniowy; splot kołowy ważony; dyskretna transformata Fouriera uogólniona

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2021
• Tom: Vol. 69, nr 4
• Strony: art. no. e137726
• Opis fizyczny: Bibliogr. 24 poz., rys., tab.

Twórcy

autor

Yi Hua

• School of Mathematics and Physics, Jinggangshan University, Ji’an, 343009, P.R. China

• https://orcid.org/0000-0002-7121-2890

autor

Ru Yu-Le

• School of Mathematics and Physics, Jinggangshan University, Ji’an, 343009, P.R. China

autor

Dai Yin-Yun

• School of Mathematics and Physics, Jinggangshan University, Ji’an, 343009, P.R. China

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).